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Assertion (A) : Divergence theorem is applicable for both static and time varying fields.

Reason (R) : It is used to find enclosed charge from the knowledge of either \(\overline{D}\) or \(\overline{E}\).

  • A.Both (A) and (R) are true and (R) is the correct explanation of (A).
  • B.Both (A) and (R) are true, but (R) is not correct explanation of (A).
  • C.(A) is true, but (R) is false.
  • D.(A) is false, but (R) is true.

Answer: A

Both statements are true and the reason explains the assertion (option A). The divergence theorem is a mathematical identity for any vector field, so it holds for static and time-varying fields alike.

The reason gives its use: with Gauss's law, the flux of \(\overline{D}\) through a closed surface (or of \(\overline{E}\) times the permittivity) equals the enclosed charge, so the theorem is used to find that charge. Options B, C and D deny one of the statements.

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